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\title{Causal Inference Methods for Estimating Long Term Health Effects of Air Quality Regulations}

\date{}
\author{
Corwin Matthew Zigler\thanks{Harvard TH Chan School of Public Health}
\and Chanmin Kim $^*$
\and Christine Choirat \thanks{Harvard University}
\and John Barret Hansen$^\dagger$
\and Lauren Hund \thanks {University of New Mexico}
\and Jonathan Samet\thanks{Keck School of Medicine, University of Southern California}
\and Gary King$^\dagger$
\and  Francesca Dominici$^*$
}

\begin{document}

\section{a table analogous to the Table 1 of the report}

\begin{table}[h]
\caption{Variables Table}\label{datatab}
\begin{tabular}{lcccc} \hline \hline
 & \multicolumn{2}{c}{\underline{Have scrubbers (n=70)}} & \multicolumn{2}{c}{\underline{Have no scubber (n=202)}} \\
  & Mean & SD & Mean & SD \\ \hline
  
   \underline{Monitor Data} \\
 Average Ambient \PMTwo 2005 & 11.59 &3.88&13.16&2.67\\ 
 Average Temperature 2004 &13.05&4.73&13.74&3.55\\ 
 Average Barometric Pressure 2004 &718.45&52.71&741.02&24.16\\ 
 
 \\ \underline{Power Plant Level Data} \\
Total \SOTwo Emission 2005 &1320.03& 1823.4&2204.04&2526.16\\ 
Total \NOx Emission 2005 &917.75&774.03&599.86&554.98\\ 
Total \COTwo Emission 2005 &565349&475743&387323.9&374378.2\\ 

 \\ \underline{Unit Level Data} \\
\NOx Scrubber Installation, Jan. 2005  &0.89&0.3&0.8&0.36\\ 
Average Heat Input 2004 &5501996&4623661& 3808147&3669536\\ 
Phase II Indicator 2004 &0.83&0.36&0.76&0.4\\ 
Total Operating Time 2004 &7697.35&650.73&7371.54&1000.96\\ 
Sulfur Content in Coal 2004 &1.13&0.89&0.66&0.45\\ 


\end{tabular}
\end{table}

\section{Can you double check the text I wrote in the section titled "Defining the Intervention: SO2 
Scrubber Installation" and provide the histogram that used to appear in your paper}
We have total 272 power plants (not 400 power plants) and among them, 70 power plants are treated.

See Figure \ref{histogram}.

\begin{figure}[h]
\center
\caption{Histogram}
\includegraphics[width=.7\textwidth]{Figures/histogram.pdf}\label{histogram}
\end{figure}

\section{Histograms of the estimated propensity scores for treated and untreated facilities }

See Figure \ref{ps}.

\begin{figure}[h]
\center
\caption{Histograms}
\includegraphics[width=.5\textwidth]{Figures/pscore.pdf}\label{ps}
\end{figure}

\section{Figures like the one that currently appears as Figure 5 of the report for the total and mediated effects}
See Figure \ref{effect}

\begin{figure}[h]
\center
\caption{Causal Effect}
\includegraphics[width=\textwidth]{Figures/mediated_effect.pdf}\label{effect}
\end{figure}

\section{Is it easy to get ATT analogs to the effects you currently report in the multiple mediator paper?}

See Figure \ref{att}

\begin{figure}[h]
\center
\caption{Causal Effect}
\includegraphics[width=\textwidth]{Figures/mediated_effect_att.pdf}\label{att}
\end{figure}


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